Objective: The objective of this subject is to make the students aware of the numerical methods for the solution of scientific problems which cannot be solved analytically.
Interpolation : Existence, Uniqueness of interpolating polynomial, error of interpolation – unequally spaced data; Lagrange’s formula, Newton’s divided difference formula. Equally spaced data : finite difference operators and their properties, Gauss’s forward and backward, Sterling’s formulae – Inverse interpolation – Hermite interpolation.
Differentiation : Finite difference approximations for first and second order derivatives.
Integration : Newton-cotes closed type methods; particular cases, error terms – Newton cotes open type methods – Romberg integration Gaussian quadrature; Legendre formulae.
Solution of nonlinear and transcendental equations: Regula Falsi method, Newton-Raphson method, Newton Raphson method for system of nonlinear equations.
Solution of linear algebraic system of equations: LU Decomposition, Gauss-Seidal methods; solution of tridiagonal system. Ill conditioned equations. Eigen values and eigen vectors : Power and Jacobi methods.
Solution of Ordinary differential equations:
Initial value problems: Single step methods; Taylor’s, Euler’s, Runge-Kutta methods, Implicit Runge Kutta methods Boundary value problems: Finite difference methods, Shooting method.
1. Jain, Iyengar and Jain : Numerical Methods for Engineers and Scientists, Wiley Eastern, 1995.
2. S. D. Cante and C. de Boor, Elementary Numerical Analysis, an algorithmic approach, McGraw-Hill, 2000.
1. Gerald and Wheatley : Applied Numerical Analysis, Addison-Wesley ,1999.
2. Aitkinson : Numerical Analysis, John Wiley and Sons , 1984.